4 more than a number is 12

Answer:

a) The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

b) The null hypothesis is [tex]H_0: \pi_1 - \pi_2 = 0[/tex] and the alternate hypothesis is [tex]H_1: \pi_1 - \pi_2 \neq 0[/tex].

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Females:

49% from a sample of 600. So

[tex]\pi_1 = 0.49, s_{\pi_1} = \sqrt{\frac{0.49*0.51}{600}} = 0.0204[/tex]

Males:

41% from a sample of 500. So

[tex]\pi_2 = 0.41, s_{\pi_2} = \sqrt{\frac{0.41*0.59}{500}} = 0.022[/tex]

Test if there is a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade.

From here, question b can already be answered.

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0. So

[tex]H_0: \pi_1 - \pi_2 = 0[/tex]

At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So

[tex]H_1: \pi_1 - \pi_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = \pi_1 - \pi_2 = 0.49 - 0.41 = 0.08[/tex]

[tex]s = \sqrt{s_{\pi_1}^2 + s_{\pi_2}^2} = \sqrt{0.0204^2 + 0.022^2} = 0.03[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.08 - 0}{0.03}[/tex]

[tex]z = 2.67[/tex]

Question a:

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.08, which is P(|Z| > 2.670, which is 2 multiplied by the p-value of Z = -2.67.

Looking at the z-table, Z = -2.67 has a p-value of 0.0038.

2*0.0038 = 0.0076

The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

Answer: b d a

Step-by-step explanation:

B

D

A

Answer:

g(x) = f(x + 2)

Step-by-step explanation:

The x value has been translated by 2

Feel free to mark it as brainliest :D

9514 1404 393

Answer:

  (0, c)

Step-by-step explanation:

Compare the given equation to the vertex form equation ...

  y = a(x -h)^2 +k . . . .  quadratic with vertex (h, k)

You have ...

  y = ax^2 +c

Matching these forms, we see that h=0, and k=c. Then the vertex is ...

  (h, k) = (0, c)

Answer:

10.5

Step-by-step explanation:

The answer for this question is 6.25

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

tan 30°= root 3/ 3

r²=x² + y²

r²= 4root3 ² + 12²

r²= 48 +144

r²= 192

ŕ= 8root3

so the bottom is 12...

the other side is 4root3

[tex]4 \sqrt{3} [/tex]

and hypotenuse is 8root3

[tex]8 \sqrt{3} [/tex]

Answer: 282.743 in2

Step-by-step explanation:

Answer:

s = 32

Step-by-step explanation:

s - 12 = 20

s (- 12 + 12) = 20 + 12

s = 32

Step-by-step explanation:

s-12=20

s=20+12

s=32

Hope it helps.

Hi there!

[tex]\large\boxed{\text{System G.}}[/tex]

For a system to have an infinite number of solutions, both expressions must be equal. We can go through each system and determine this:

F:

x + 2 = y

4 = 2y - x

If we rearrange so that both are in the same format, we get:

x + 2 = y

x + 4 = 2y

These cannot be equal, so they do not have infinite solutions.

G:

2y + 6 = 4x

-3 = y - 2x

Rearrange:

2y + 6 = 4x

-y - 3 = -2x

We can try to make the bottom equation look like the top equation by multiplying all terms by -2. We get:

2y + 6 = 4x. This is the same as the top, so G has infinite solutions.

Just to be sure, we can go through the others:

H:

y + 3 = 2x

4x = 2y - 3

Rearrange:

y + 3 = 2x

2y - 3 = 4x. Cannot be equal to the other equation.

J:

y = 2x - 5

y = 2x - 2. Not equal.

The correct answer is G.

Answer:

x = 14

Step-by-step explanation:

The polygon given has 6 sides

Sum of interior angles of a 6-sided polygon = 180(n - 2)

substitute n = 6 into 180(n - 2)

Sum of the polygon = 180(6 - 2) = 720°

Thus:

10x + 8x - 16 + 12x - 8 + 7x + 2 + 9x + 4 + 6x + 10 = 720

Add like terms

52x - 8 = 720

52x = 720 + 8

52x = 728

x = 728/52

x = 14

Answer:

D

Step-by-step explanation:

because I remember doing this before

Answer:

[tex]\frac{4}{20}[/tex] or 0.2 or 20%

Step-by-step explanation:

For only two tests to be needed this means that the first test would need to come back as negative and the second test would be to come back as positive. Therefore, to find the probability of this happening we first need to find the probability of each individual test and multiply them together.

The first test needs to come back negative, there are four negative individuals out of the total 5 that are in the group. Therefore, the probability of the first test is 4/5.

Now we remove the individual that has just been tested and we are left with 4 total subjects in the group, of which only 1 is positive. Therefore, the probability of the second test is 1/4. Now we need to multiply these two probabilities together to get the probability of only needing two tests.

[tex]\frac{4 * 1}{5 * 4} = \frac{4}{20}[/tex] or 0.2 or 20%

From 2 to 101 , the perfect square numbers are ,

Total number of possible outcomes = 100.

Total number of favourable outcomes = 9 .

Hence ,

→ P ( of getting perfect square ) = 9/100

Answer:

step 3 didn't divide by 2

Step-by-step explanation:

in step

[tex] \frac{ - 8 + \sqrt{100} }{2} = \frac{ - 8 + 10}{2} = 1 \\ \frac{ - 8 - \sqrt{100} }{2} = \frac{ - 8 - 10}{2} = - 9[/tex]

Answer:

2pi

Step-by-step explanation:

Right on edg assignment

Answer:

[tex]Area =55.4ft^2[/tex]

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

[tex]\tan(60) = \frac{4\sqrt 3}{x}[/tex]

Solve for x

[tex]x = \frac{4\sqrt 3}{\tan(60)}[/tex]

[tex]\tan(60) = \sqrt 3[/tex]

So:

[tex]x = \frac{4\sqrt 3}{\sqrt 3}[/tex]

[tex]x = 4[/tex]

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

[tex]Base = 4\sqrt 3[/tex]

[tex]Height = 4[/tex]

So, the area of the rhombus is 4 times the area of 1 triangle

[tex]Area = 4 * \frac{1}{2} * Base * Height[/tex]

[tex]Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4[/tex]

[tex]Area =2 * 4\sqrt 3 * 4[/tex]

[tex]Area =55.4ft^2[/tex]

Answer:  1,953,125

This is one single value and it is just a bit under 2 million.

Or more accurately, it's a bit over 1.9 million.

===========================================================

Explanation:

Note that dividing any term by its previous term gets us the common ratio

The r value must stay the same the entire time, or else the sequence isn't geometric.

The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)

-----------------

To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.

If we tried n = 2 for instance, then we find the 2nd term is

5(-5)^(n-1) = 5(-5)^(2-1) = -25

which matches what your teacher gave you. I'll let you verify the other terms.

-----------------

The last thing we need to do is plug in n = 9 and simplify

5(-5)^(n-1)

5(-5)^(9-1)

5(-5)^8

5(390625)

1,953,125  this is one single value (rather than 3 separate values)

Answer:

$72.70

Step-by-step explanation:

bill was $56.80

tip was 20% so was 56.80/ 5( because 5 of 20% will make 100%)= $11.36

tax was 8% so was 56.80*8/100= $4.54

total money paid

56.80+4.54+11.36 = 72.70

Answer:

The mean number of tiebreakers is of 35.2 and the standard deviation is of 5.44.

Step-by-step explanation:

For each set, there are only two possible outcomes. Either it goes to a tiebreak, or it does not. The probability of a set going to a tiebreak is independent of any other set, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The probability that a tennis set will go to a tiebreaker is 16%.

This means that [tex]p = 0.16[/tex]

220 randomly selected tennis sets

This means that [tex]n = 220[/tex]

What is the mean and the standard deviation of the number of tiebreakers?

[tex]E(X) = np = 220*0.16 = 35.2[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{220*0.16*0.84} = 5.44[/tex]

The mean number of tiebreakers is of 35.2 and the standard deviation is of 5.44.

Answer:

y= (-6/5)x -2

Step-by-step explanation:

y=mx+b , where m is the slope, and b is the y -intercept

the y -intercept is where the line intersects the y-axis so b = -2

the slope m= y(rise) /x(run)  = 6/-5 = -6/5 ( to find the slope you have to know how to get from any point on the line to another point on the same line; start at point (0,-2) go up 6(y-rise) and to the left 5(x-run) at point (-5,4))

y= (-6/5)x -2

Answer:

the answer is a!

Step-by-step explanation:

Answer:

8ft is the diameter so the radius would be half of that, so it's 4ft. Now substitute

[tex]\pi4 {}^{2} [/tex]

now solve 4^2=16 now multiply it by 3.14 (pi). 16×3.14= 50.24

Answer:

either 22/60 or .3666 recurring

Step-by-step explanation:

All you are doing is converting minutes to hours basically, so all you have to do is divide 22 by 60.

Answer:

b

Step-by-step explanation:

because the price of money is maximum 2,500

Answer:i dont know

Step-by-step explanation:

Answer:

100 pi cm^2

or approximately 314 cm^2

Step-by-step explanation:

The surface area of a sphere is given by

SA = 4 pi r^2

The radius is 5

SA = 4 *pi * 5^2

SA = 4*pi(25

SA = 100 pi cm^2

If pi is 3.14

SA = 100 *3.14 = 314 cm^2

[tex]\large\fbox{\underline{Surfαcє αrєα σf sphєrє ís 314 cm ².}}[/tex]

☞ Rαdíus σf sphєrє = 5 cm

☞ Surfαcє αrєα σf sphєrє

☞ Surfαcє αrєα σf sphєrє = 4 π r ²

usíng thє fσrmulα

surfαcє αrєα σf sphєrє = 4 π r ²

suвstítutє thє vαluєs

surfαcє αrєα σf sphєrє = 4 × 3.14 × ( 5×5 ) cm ²

mutíplчíng thє vαluєs

surfαcє αrєα σf sphєrє = 100 cm² × 3.14

Hєncє , Surfαcє αrєα σf sphєrє ís 314cm ².

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Researchers must increase the response rate to achieve a narrower confidence interval. Because we see that the trust gap is inverse to sample size. We must increase data in estimating a narrower 95-percent trust range. Since the sample has increased, its error margin has decreased, this reduces the width of the trust interval.